Weighted threshold secret sharing schemes

In a secret sharing scheme, each participant receives a share of a secret i n such a way that only authorized subsets can reconstruct the secret. The i nformation rate of a secret sharing scheme is the ratio between the size of the secret and the size of the shares given to the participants. In a weig hted threshold scheme each participant has his or her own weight. A subset of participants is authorized to reconstruct the secret if the sum of their weights is greater than or equal to the threshold. This paper deals with w eighted threshold schemes, mainly the properties related to the information rate. A complete characterization of the access structures of weighted thr eshold schemes when all the minimal authorized subsets have at most two ele ments is presented. Lower bounds for the optimal information rate of these access structures are given. (C) 1999 Published by Elsevier Science B.V. Al l rights reserved.